Final answer:
Using the Pythagorean theorem for the right triangle formed by the radius, tangent, and line from the circle's center to the point, the length of the tangent is found to be 3 cm, which is not listed in the provided options.
Step-by-step explanation:
The question asks for the length of the tangent from a point outside a circle to the circle itself, which involves using the Pythagorean theorem in a right triangle formed by the radius, tangent, and the line from the circle's center to the point outside the circle.
The diameter of the circle is given as 8 cm, this makes the radius 4 cm (half of the diameter). The distance from the circle's center to the point is 5 cm. Using the Pythagorean theorem, the tangent length (t) can be calculated as follows:
t2 = 52 - 42
t2 = 25 - 16
t2 = 9
t = √9
t = 3 cm
However, none of the options provided in the question include 3 cm as a possible answer, indicating either an error in the formulation of the question or the options provided.